Transmission lines, with their characteristic loss of signal as well as inherent time delay, may create problems in designing systems that employ a plurality of signals that may undergo delay and distortion. Modern computers, for example, are systems that employ a plurality of electrical signals and for which transmission line properties, such as delay, must be considered. Both digital computer chips and the circuit boards for interconnecting the signals of these computer chips may have transmission line effects.
Typical signals when used to generate inputs to transmission lines generally exhibit delay or propagation times that are not easily determinable. The propagation velocity of these waves is also variable with displacement along the transmission line.
Changing or modifying the delay of an electromagnetic transmission line usually involves changing the physical length of the line; changing the width, thickness and spacing of the line; modifying the capacitance of the line at points spaced along the line; or altering the transmission line by changing the dielectric constant of the media surrounding the line""s conductor. None of these methods, however, lend themselves to applications where it may be desirable to vary, change, or otherwise modify the propagation time of a pulse applied to a lossy transmission line.
Current transmission line technology is based on the theory of lossless transmission and assumes that pulse propagation speed along a transmission line is constant. This assumption, however, significantly restricts design options for implementing delay lines in electronic circuits. Specifically, delay lines are currently implemented by increasing the signal path (so the signal takes longer to arrive at a destination) or by adding additional active circuitry to slow down a signal. In either case, changing the amount of delay may be difficult and/or expensive because it may require redesigning and changing circuitry. Moreover, there is often no way to controllably vary delay based on different input conditions. Therefore, it would be advantageous to have the ability to implement a delay line that could controllably vary a delay time or attenuation based on different input conditions and that could be implemented simply and inexpensively.
Currently known methods for measuring transmission line parameters, such as resistance, inductance, capacitance, and conductance, typically require specialized instrumentation that may be very expensive. Therefore, it would be advantageous to have the ability to measure such parameters in a simple manner using, for instance, inexpensive multipurpose instrumentation generally available in electronics laboratories such as an oscilloscope or a signal wave-form generator.
The amount of delay in networks, including broad band networks, is often a primary design factor. Current design techniques for analyzing the length of delay in non-inductive and inductive transmission line networks, however, are notoriously inaccurate; therefore, it would be advantageous to have the ability to employ a simple formula to calculate the total delay or attenuation in non-inductive as well as inductive networks with a high degree of accuracy. It would be further advantageous if such a method could be utilized in computer-aided-design (CAD) systems.
In one respect, the invention is a method for transmitting a waveform having an essentially constant propagation velocity along a transmission line. As used herein, xe2x80x9cwaveformxe2x80x9d shall be read broadly to mean any energy signal, or representation thereof. As used herein, xe2x80x9ctransmission linexe2x80x9d shall be read broadly to refer to any media capable of transmitting a particular waveform. Transmission line may refer to a broad range of media including, but not limited to, electrically conducting and mechanically vibrating media. According to the method, an exponential waveform is generated. The exponential waveform is characterized by an exponential coefficient xcex1. The waveform is applied to the transmission line to transmit the waveform at an essentially constant propagation velocity, and the propagation velocity is related to xcex1 and a transmission parameter of the transmission line. As used herein, xe2x80x9ctransmission parameterxe2x80x9d shall be read broadly to refer to any discemable characteristic of the media making up the transmission line.
In other respects, the transmission parameter may include inductance, resistance, capacitance, conductance, or any combination thereof of the transmission line. The propagation velocity may be related to a in accordance with several different equations such as, but not limited to, those described herein. An attenuation coefficient of the waveform may also be related to cc in accordance with several different equations such as, but not limited to, those described herein. The transmission line may include an electrical conductor. The transmission line may include a conducting trace. The transmission line may include a delay line. The transmission line may include an interconnect. The transmission line may include an acoustic medium. The transmission line may include a diffusion medium. The method may also include varying a in response to an input signal to the waveform generator. The method may also include determining the propagation velocity and calculating the transmission parameter using the propagation velocity and the exponential coefficient. Determining the propagation velocity may include receiving propagation information from the transmission line using one or more receiving elements coupled to the transmission line. The one or more receiving elements may include a threshold detector. The method may also include determining an impedance discontinuity of the transmission line and its location using the exponential coefficient, the propagation velocity, and the transmission parameter. The method may also include varying the exponential coefficient xcex1 to encode information onto the waveform. The method may also include monitoring modulated propagation velocity to decode the information. The method may also include monitoring modulated attenuation to decode the information.
In another respect, the invention is a method for transmitting a waveform along a transmission line. An exponential waveform is generated. The exponential waveform is characterized by an exponential coefficient xcex1. The waveform is applied to the transmission line to transmit the waveform such that an attenuation constant of the waveform is related to xcex1 and a transmission parameter of the transmission line.
In other respects, the method may also include determining an impedance discontinuity of the transmission line and its location using the exponential coefficient; the attenuation constant, and the transmission parameter.
In another respect, the invention is a method for calculating an unknown waveform transmission characteristic from two known waveform transmission characteristics. An exponential waveform is constructed that is capable of being transmitted along a transmission line with an essentially constant propagation velocity. The propagation velocity is related to a transmission parameter of the transmission line and to an exponential coefficient of the waveform. The transmission parameter defines a first unknown waveform transmission characteristic, the propagation velocity defines a second unknown waveform transmission characteristic, and the exponential coefficient defines a third unknown waveform transmission characteristic. One of the three unknown waveform transmission characteristics is calculated by setting the remaining two of the three unknown waveform transmission characteristics equal to two known waveform transmission characteristics.
In other respects, the method may also include generating the exponential waveform and transmitting the waveform along the transmission line. The transmission line may include a model transmission line. The remaining two of the three unknown waveform transmission characteristics may be set equal to two known waveform transmission characteristics by measurement. One of the two known waveform transmission characteristics may include the transmission parameter and the other of the two known waveform transmission characteristics may include the propagation velocity. The propagation velocity may correspond to a desired delay time for the transmission line, and the exponential coefficient may be calculated to yield a computed exponential coefficient. The method may also include inputting an exponential waveform with the computed exponential coefficient onto the transmission line to achieve the desired delay time. The transmission line may include a model transmission line, and the method may further include fabricating an actual transmission line to correspond to the model transmission line. The actual transmission line may be configured to transmit an exponential waveform having the computed exponential coefficient to achieve the desired delay time. The model transmission line may include a computer aided design model. One of the two known waveform transmission characteristics may include the exponential coefficient, and the other of the two known waveform transmission characteristics may include the propagation velocity. The propagation velocity may be measured with an exponential waveform having the exponential coefficient, and the transmission parameter may be calculated. The transmission parameter may include inductance, resistance, capacitance, conductance, or any combination thereof of the transmission line.
In another respect, the invention is a method for calculating an unknown waveform transmission characteristic from two known waveform transmission characteristics. An exponential waveform is constructed that is capable of being transmitted along a transmission line with an attenuation constant related to a transmission parameter of the transmission line and to an exponential coefficient of the waveform. The transmission parameter defines a first unknown waveform transmission characteristic, the attenuation constant defines a second unknown waveform transmission characteristic, and the exponential coefficient defines a third unknown waveform transmission characteristic. One of the three unknown waveform transmission characteristics is calculated by setting the remaining two of the three unknown waveform transmission characteristics equal to two known waveform transmission characteristics.
In other respects, one of the two known waveform transmission characteristics may include the transmission parameter and the other of the two known waveform transmission characteristics may include the attenuation constant. The attenuation. constant may correspond to a desired attenuation for the transmission line, and the exponential coefficient may be calculated to yield a computed exponential coefficient. The method may also include inputting an exponential waveform with the computed exponential coefficient onto the transmission line to achieve the desired attenuation.